Sort off. But its more on sonys first party output. Cus they are the market leader and have a big ps4 installbase that is itching to upgrade. The ps4 owners dont only have to be convinced that xbox is doing better but that they are better than sony if they are to jump ship.
PS Studios output matters as well, but nowhere near as much. Sony have a proven track record and with GoW Ragnarok getting yet another extremely high review score, people are at the point where they have a considerable amount of trust in PS first party output.
XB doesn't have this luxury, and with the Halo Infinite launch and handling since, they've pretty much got just expectations still. Until XB puts out a few undeniably amazing first party games, or starts and keeps putting out widely considered worthy games, they won't have near the confidence from people as PS does.
PS would need to put out a couple AAA games in a row that flat out bombed hard for people to feel uneasy about their future games. While that's possible it's very unlikely based on what we've seen for over a decade now.